Rational Functions

Simplify Rational Expressions

100

Simplify.

(j² + 12j + 20)/(j + 10)

j + 2

200

Simplify.

(x + 10)/(x² + 10x)

1/x

300

Simplify.

(x - 7)/(x² - 4x - 21)

1/(x + 3)

400

Simplify.

(x³ - 18x² + 32x)/(x² - 4)

x(x - 16)/(x + 2)

500

Simplify.

(4x³ - 24x² + 32x)/(8x - 16)

x(x - 4)/2

Multiply or Divide Rational Expressions

100

Multiply.

1/x * x/4

1/4

200

Multiply.

(4x - 5)/(4x² - 5x) * x

1

300

6x/(2x - 5) ÷ 2

3x/(2x - 5)

400

Simplify.

(x² + 4x + 3)/8x ÷ (x + 3)

(x + 1)/8x

500

(12x³ + 3x²)/(4x - 5) ÷ (48x⁴ - 3x²)

1/((4x - 5)(4x - 1))

Add or Subtract Rational Expressions

100

Add.

2/v + v/2

(v² + 4)/2v

200

Subtract.

1/x - 3/y

(y - 3x)/xy

300

Simplify.

u - 6 + u⁴/2

(2u - 12 + u⁴)/2

400

Add.

6/(7q - 2) + 3

21q/(7q - 2)

500

Subtract.

c/(c + 4) - 7

(-6c - 28)/(c + 4)

Graph Rational Expressions

100

Find the excluded value.

f(x) = 7/x

x = 0

200

Find the excluded value.

f(x) = (x+5)/(x - 3)

x = 3

300

Find the vertical asymptotes.

g(x) = x/(x² - 7x - 8)

x = 8, x = -1

400

Find the horizontal asymptote. 

f(x) = (5x² - 9)/(6x³ - 1)

y = 0

500

Find the oblique asymptote.

f(x) = (x² - 8x + 3)/(x - 2)

y = 1x - 6

Solve Rational Equations

100

Solve.

(x + 6)/4 = (x + 5)/6

x = -8

200

Solve.

3/(3h + 9) = h/(5h - 1)

h = 1

300

Solve. 

x/(10x + 49) = 1/(x + 10)

x = -7, or x = 7

400

Solve.

x/3 + 1/2 = (3x + 1)/6

x = 2

500

Solve.

x/(x - 5) = 5/(x - 5) + 2

No solution